Realisitically, this has not been the solution implmented (in the EU & US, at least). In the EU, it is even more crucial as the "solutions" to this problem are applied to state finances as well as financial institutions.

In terms of policies, there are two competing approaches: (1) Reduce the size of "too-big-to-fail" institutions. (2) Regulate them more heavily (or some other strategy) so that they will not fail. In the EU, this is being applied to states, not just financial institutions. Rules that (supposedly) reduce catastrophic risk.

Almost all seripous policy proposals are in the no. 2 category. Tighten regulation, reduce the risk of failure. Tighter regulation lends to stronger incumbents and larger average company size so by doing 2, you are probably doing the opposite of 1.

As I said, I don't know what Bernie's proposal is or how mature it is as a policy (as opposed to a politician statement). It would be notable if a left wing politician propsed loosening bank regulations, though definitely not impossible or unreasonable.